What is Length: Definition and 1000 Discussions

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.
Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in.
Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object.Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).

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  1. J

    Find mass per unit length of a string graphically

    Homework Statement frequency, Tension, mass, mode of vibration Homework Equations v = sqrt(T/μ) The Attempt at a Solution length of string is 2.14m weight .00247kg mass per unit length (μ) .00089 However, I need to confirm this graphically. I solved for mass per unit length μ = T/V^2 or...
  2. K

    Lorentz Transformation, Time Dilation, Length Contraction

    Homework Statement [/B] A spaceship is approaching Earth from the far side of the sun. The Earth and sun are 8 light minutes apart and the ship is traveling at .8c. Two events are indisputable. 1) the ship is at the sun 2) the ship is at the earth. Assume that the Earth and sun are at rest...
  3. N

    Does displacement=shortest length of position (final-initial)?

    Homework Statement if displacement is the shortest distance between two point then that would also meant that it is equivalent to the hypotenuse when using phytogaras theorem right?. but why isn't displacement the shortest length between two point ?because Xinitial - Xfinal couldn't posibly be...
  4. M

    Length contraction and time dilation from Lorentz S

    I'm trying to understand special relativity well enough to explain it to others, ANY others, including myself. I am trying to use Robert Resnick's Introduction to Special Relativity to inform my thinking. In introducing length contraction, he introduces L' as the length measured by an observer...
  5. Sentosa

    I How Does Length Contraction Affect Train Wheel Rotation at Near Light Speeds?

    There's a section in my astronomy book on relativity. The image shows a train traveling at a slow speed and a second image of the train approaching the speed of light. The text says the second train is length contracted, but only in the horizontal direction. In the vertical direction the train...
  6. RabbitWho

    Finding distance of image from mirror given focal length

    Homework Statement An object is at a very large distance from a concave mirror of focal length 40cm. Find the distance from the image to the mirror. Is the image real or virtual? Homework Equations 1/u + 1/v = 1/f The Attempt at a Solution [/B] 1/u + 1/v = 1/40 The image has to be real...
  7. D

    Length covered by block after collision

    Homework Statement Board ##A## is placed on board ##B## as shown. Both boards slide, without moving w.r.t each other, along a frictionless horizontal surface at a speed of ##6 \text{m/s}##. Board ##B## hits a resulting board ##C##, "head-on". After the collision, board ##B## and ##C## stick...
  8. Stephanus

    B Discrete definitions of Physics Standard Units

    Dear PF Forum, Perhaps it's not a question, just a light discussion. Time From this, we get the standard time https://en.wikipedia.org/wiki/Caesium_standard, it's 9,192,631,770 ticks per second. I think this number should be discreet. No need to tune it to some figures after decimal point. Is...
  9. Turbodog66

    Length of Curve Between Points: Exploring r(t)

    Homework Statement Consider the path r(t) = <10t,5t2,5ln(t) defined for t >0. Find the length of the curve between (10,5,0) and (20,20,5ln(2)) Homework Equations L= ∫ab |r'(t)|dt The Attempt at a Solution r'(t) = <10, 10t, 5/t> t values are 1 and 2 based on the x values for the points...
  10. hsdrop

    B How have we figured out the Plank length of the universe?

    how have we figured out plank length of the universe ?and know its that size ?
  11. T

    MHB Help finding length of perpendiculars in a box of known dimension

    For a research problem, I'd like a way to find the distance of each of 4 lines perpendicular to one of 4 walls connected to a point that is within a box of known dimension. I know the distance from the center of each wall to the point of interest (C1 to C4), but I do not know the angle this...
  12. M

    MHB What is the length of DC in this trapezium?

    In the trapezium ABCD shown in the figure, AB = (x + 3) cm, DC = (2x − 3) cm and BE = EC. If the area of the trapezium is 15 cm2, find the length of DC to the nearest first decimal place. Take $\sqrt{19}$ = $4.36$ Have I done correctly, Okay first we know that area of a trapezium $15 =...
  13. ATY

    How Accurate is the Integral Length Calculation in Turbulence Studies?

    . ##\require{color} \color{white} \colorbox{crimson} {Mod Note: to see images in this post displayed correctly, click on Reply and view this in editor}## Hey guys, I need your help. It is about the integral length of turbulence flow. So we got data from some wind measurement, recorded at...
  14. Babbeus

    I Lorentz derivation of length contraction in electrodynamics

    Here is a quote from this website: My question is: is this derivation of length contraction considered to be sound and correct today? Are they treated in modern textbooks?
  15. Zahidur

    I Subbing Planck length into length contraction equation?

    I was wondering if it is possible to work out the maximum amount of energy an object with mass can have using the length contraction equation (i.e. "actual" length divided by Lorentz factor). The way I thought of doing this was by rearranging e = mc^2 to get c^2 = e/m. Then, substitute e/m into...
  16. C

    Change in length due to temperature

    Homework Statement in the notes , i was told that ∂A is the resistance of aluminium rod...I'm wondering the change length of steel rod that we can 'see' is ∂ st or ∂T(st) ? Homework EquationsThe Attempt at a Solution I think the change length of steel rod that we can 'see' is ∂ st ?
  17. I

    Balancing Mass: Solving for Bar Length

    Homework Statement The bar has a mass of 3 grams/cm. When a mass of 15 grams is hung on the left side, the system is balanced. Calculate the length of the bar. Homework Equations F1*r1 = F2*r2 The Attempt at a Solution I thought that the moment on the left should be equal to the moment at the...
  18. R

    I Meaning of inelastic scattering length

    Hello, what is the physical meaning of the scattering length? I know this question was discussed here before but I still have questions. This quantity is listed in table 1 of this paper: http://rpd.oxfordjournals.org/content/132/1/29.full.pdf. I need to clarify a few things: does scattering...
  19. A

    I Why can't you use Simultaneity when doing Length Contraction

    Suppose that frame O' moves at speed v = 0.6c relative to frame O. A rod with two balls is attached to its ends is 10 meters long in its rest frame, O'. Length contraction will tell you that in frame O, the rod is 8 meters long. But aren't the two balls at the ends "events"? They are clearly...
  20. Einstein's Cat

    B Planck's Length, Length Contraction?

    Would Planck's length be subject to length contraction if an object hypothetically of the length had a velocity near c? I suspect that it won't becuase Planck's length is defined by the invariant, physical constants of G, c and the reduced Planck's constant. Thus, Planck's length would not be...
  21. F

    System of linear inequalities to find a vector

    Homework Statement Let P be the set of (x,y,z)^t in R^3, which satisfies the following inequalities: -2x+y+z <=4 x-2y+z<=1 2x+2y-z<=5 x>=1 y>=2 z>=3 Homework Equations I want to find the vector in the set with the maximal length. The Attempt at a Solution I have transformed the linear...
  22. J

    I Decomposing the arc length of a circular arc segment

    A particle travels along a circular arc segment centered at the origin of the Cartesian plane with radius R, a start angle θ1 and an end angle θ2 (with θ2 ≥ θ1 and Δθ = θ2 - θ2 ≤ 2π). The total distance traveled is equal to the arc length of the segment: L = R(Δθ). I would like to find the...
  23. Tazerfish

    How Do Length-Adjustable Gas Springs Work?

    I was uncertain wether to put this in the general physics forum, but I decided against it. How do length adjustable gas springs(like for example in office chairs)work ? I know how gas springs work and i even have an idea how length adjustable ones could work. Since you hear a "gas flowing...
  24. F

    Why Prandlt Mixing Length Theory works at all?

    There are several unreasonable assumptions in the formulation of the Prandlt Mixing Theory. However, it works reasonably well for simple 1-D flow. An attempt to explain why is given by Davidson in his book 'Turbulence', on page 122 - 124, section 4.1.4. It's stated that it still works because...
  25. H

    How was the reactor length determined here?

    I've recently been reading this paper (a free version is available here). I've been trying to work out how they came to the 128m length, but I just can't. Feel like it's been just beyond my grasp for a long time and it's been driving me mad. Any help would be appreciated. Thanks in advance.
  26. EmilyBergendahl

    Double Slit: Separation and Path Length

    Homework Statement A double slit apparatus is held 1.2 m from a screen. (a) When red light (λ = 600 nm) is sent through the double slit, the interference pattern on the screen shows a distance of 12.5 cm between the first and tenth dark fringes. What is the separation of the slits? (b) What...
  27. smodak

    I Length of bases in Polar coordinates

    According to this video the length of basis is r. It grows as we further from the origin . Why?
  28. G

    I How can gravitational waves be detected if spacetime itself warps?

    Hi, First: I'm pretty sure my question has been asked numerous times, so I'm absolutely happy with links to other threads. I've used search but it didn't come up with satisfying responses, probably mainly because I don't really know what search terms to use. So the question is: How can a...
  29. R

    B Some basic questions about length contraction in SR

    Imagine there are two space ships, Ship A and Ship B. Ship A sees Ship B traveling at 0.865c towards him. (And of course vice versa) From Ship A's FOR there is a marker 9,000,000 km away which is at rest wrt Ship A. The marker, Ship A and the path of Ship B therefore form a straight line. When...
  30. paulmdrdo

    Finding the length of the circuit.

    Homework Statement Homework Equations D = rt The Attempt at a Solution [/B] This is my attempt let d= length of the circuit 60/a mph --- speed for walking 60/b mph ----speed for riding 60/c mph ---- speed for driving d=(60/a)t1+(60/b)t2+(60/c)t3 From here I cannot continue. Kindly help...
  31. Ravi Singh choudhary

    Stress strain diagram of mild steel -- gauge length made half

    All we know the usual stress strain diagram obtained from tensile test from universal testing machine. As modulus of elasticity is material property that means till proportional limit slope will not change. As it is not a force vs elongation curve that means there will be no re-scaling to be...
  32. defaultusername

    What is the Correct Calculation for Sam's Speed at the Bottom of the Slope?

    Homework Statement Sam, whose mass is 75 kg, stands at the top of a 12-m-high, 100-m-long snow-covered slope. His skis have a coefficient of kinetic friction on snow of 0.07. If he uses his poles to get started, then glides down, what is his speed at the bottom? Homework Equations v =...
  33. W

    Compression of an object and its length.

    I have heard a claim that looks a little odd to me and I am hoping that someone can help. In the gym there are foam rollers people use, some of them are 36 inches long and some are 16 inches. The claim is that the shorter ones can withstand greater weight than longer ones and will have less...
  34. Einstein's Cat

    B Exploring Length Contraction in Higher Dimensions: A Scientific Inquiry

    Please excuse any stupidity, but I'm under the impression that objects that travel "along" 3- dimensional" space (therefore the objects are three dimensional) with velocity v are subject to length contraction. However would objects of 3+ dimensions and with velocity v still be subject to length...
  35. Zoey

    Does the length of a wire affect its resistance?

    Hello, I would think that it would, because if the wire is longer there is more of a chance of their being foreign objects interfering, which could cause resistance, right? Or no?
  36. N

    MHB Word problem: Finding The Length Of A Column Of Marching Soldiers

    An army of soldiers is marching down a road at 5 mi/hr. A messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. Assuming that the messenger rides at the rate of 10mi/hr, determine the distance from the front to the rear. Can you...
  37. edguy99

    B What is the relationship between the Planck length and black holes?

    This article is posted on twitter with the byline: "You, me, and even aliens from Alpha Centauri could arrive at the same Planck units." but does not explain why. http://www.symmetrymagazine.org/article/the-planck-scale I believe I have read (but cannot find the reference now) the following...
  38. Vidar Martinsen

    I Consequences of length contraction

    If you are in a space ship, traveling near light speed, will length contraction enable you to se astronomical events lightyears away, before it is possible to see them from earth? This because the distance is shorter for you in the spaceship and light speed is constant. Example: A star 100 ly...
  39. F

    Calculating focal length from a number of focal ratios

    Homework Statement A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam...
  40. AotrsCommander

    I How to calculate day length of a tidelocked double planet?

    Quick question: what's the calculation required for working out the day length (i.e. rotational period) of a double planet, where both planets are tidelocked to each other? Do just need to make adjustments to Kepler's Third? I've got a spread sheet set up to allow me to calculate orbital...
  41. Alex_Neof

    Determining the focal length of a compound lens

    Homework Statement A biconvex lens, L_1, with focal length of magnitude \left| f_1 \right| = 15 cm is used with a second biconvex lens, L_2, with focal length of magnitude \left| f_2 \right| = 25 cm to form a compound lens system. If the two lenses are placed in mutual contact what is...
  42. S

    Evaluate length of the spiral (Line Integral)

    Homework Statement Evaluate the length of the spiral with parametric equation ψ(t) =< 2 cost, 2 sin t, π/t >, with t ∈ [0, 2π]. Homework Equations Line integral ∫C f(x,y) dS The Attempt at a Solution f(x,y) = z = π/t ∫C π/t dS [0, 2π] are the lower and upper bounds of integration dS=...
  43. D

    Finding the Focal Length: A Homework Challenge

    Homework Statement Homework Equations 1/do+1/di=1/f The Attempt at a Solution I tried finding the distance of image at 27m and then at 30.5m and taking the difference but that didn't work.
  44. R

    Pendulum Length and Period Calculations

    Homework Statement Homework Equations T=2pi√(L/g) The Attempt at a Solution I am just making sure I am doing these right. For the first one, I used the equation to determine the length it would be on Earth. The length I got was g/pi^2 = 0.993 m. I thought that it would have to stay the same...
  45. W

    Deriving back focal length using Fermat's principle

    Homework Statement The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length Homework Equations N/A The Attempt at a Solution I've...
  46. karush

    MHB When Should Parametric Equations Be Used to Calculate Curve Length?

    Find the arc length of $$f (x)=(1/3)(x^2 +2)^{3/2}$$ On the interval [0, a] The parametric I got $$y=t$$ $$x=\sqrt{(3t)^{2/3}-2}$$ I proceeded but didnt get the answer of $$a+\frac{a^3}{3}$$
  47. S

    I Bond length of a hydrogen bond

    Hello, in ice I have read that the average bond length of the hydrogen bond is about 2 Angstroms. This is roughly twice the O-H (covalent) bond length. My question is what really determines the length of the hydrogen bond? Why wouldn't the hydrogen be drawn closer to the next water...
  48. F

    B Length contraction vs Space time

    Does length contraction means the contraction of space time?
  49. BsNLucky

    Equation for photocurrent dep. wavelength, diffusion length,

    Hey, I’m currently stuck at my research and I’d like to ask for some help. First I’ll try to introduce the measurement and the setup and then I’ll get straight to the problem. The goal is determining the diffusion length of charge carriers quantitatively in different materials. For this...
  50. A

    Small diameter water nozzle efficiency versus nozzle length

    Hello! We are 3 students working on a bachelor thesis rigth now, with the purpose to determine the efficiency for different nozzle designs. We have done several practical tests, where we have logged the water pressure and the flow out from the nozzle, and calculated the nozzle efficiency based...
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